Method and apparatus for providing welding type power

ABSTRACT

A method and apparatus for providing welding-type power includes an input circuit, a power circuit, and a controller. The input circuit receives input power and provides intermediate power. The power circuit has a power control input with at least one switch that responds to the control input. The power circuit receives the intermediate power and provides welding type output power. The controller has a set point input and a control output. The control output is connected to the power control input. The control circuit also includes a pwm module that responds to the user set point input and provided the control output. The pwm module can include a short duty cycle linearizing module. The pwm module can also include a short duty cycle charging ramp module.

FIELD OF THE INVENTION

The present disclosure relates generally to the art of welding typepower supplies. More specifically, it relates to welding type powersupplies with pulse width modulated circuits.

BACKGROUND OF THE INVENTION

There are many known types of welding-type power supplies that providewelding type power. Welding type power, as used herein, refers to powersuitable for electric arc welding, plasma arc cutting or inductionheating. Welding type power supply, as used herein, refers to a powersupply that can provide welding type power. Welding type systems areused to perform a variety of processes and used in a variety ofsettings. Welding type system, as used herein, is a system that canprovide welding type power, and can include control and power circuitry,wire feeders, and ancillary equipment.

There are a variety of welding type processes, such as TIG, GMAW, subarc, short circuit welding, catting, arc gouging and others. Somewelding type systems are designed for a single process and others aredesigned for multiple processes. Many welding systems include switchbased power circuits, such as inverters and converters. Such systemsoften include an input circuit, a power circuit, and a controller, aswell as ancillary equipment such as wire feeders, robots, etc.

Input circuit, as used herein, refers to circuits configured to receiveinput power and to provide intermediate power, and may include as partthereof components and circuits such as rectifiers, transformers,saturable reactor, converters, filters, and/or magnetic amplifiers.Power circuit, as used herein, refers to the switches and componentsthat cooperate to process power eventually provided as output power.Controller, as used herein, refers to digital and analog circuitry,discrete or integrated circuitry, microprocessors, DSPs, etc., andsoftware, hardware and firmware, located on one or more boards, used tocontrol a device such as a power supply, power source or power circuit.

Some welding type systems include a preregulator which provides a dcbus, followed by an inverter based output circuit. The preregulatorconditions the input power, and provides a known dc bus. The inverterbased output circuit receives the bus and provides the welding typepower as an output. One successful design includes a boost circuit aspart of the preregulator, and the output circuit includes an inverter,transformer, rectifier and output inductor. This type of welding typepower supply is described in U.S. Pat. No. 6,987,242 (Geissler). Otherwelding type power supplies that have inverter based output circuitsinclude U.S. Pat. No. 6,115,273 (Geissler) and Patent Publication20090230941 (Vogel), all three of which are owned by the owner of thispatent, and all three of which are hereby incorporated by reference.Other welding type power supplies include additional stages, or useother topologies for each stage (such as a buck preregulator, a combinedrectifier-boost preregulator, a chopper instead of or following theinverter, a second inverter following the first inverter, etc.

Welding systems with converters, and particularly inverters, often use aPWM (pulse width modulation) control. PWM control provides for a fixedfrequency (on time plus off time), and adjusts the duty cycle (on time)to obtain a desired output. Thus, in a forward type inverter topology,the power flow is regulated by modulating the duty cycle of the mainpower switches. The duty cycle is the ratio of the time the switch is onversus the total cycle time of the switching event.

A typical implementation of a welding type system is shown in FIG. 1 andincludes a controller 101 that takes as inputs a required currentsetpoint and actual output values, and calculates the voltage command(or command signal) that will dynamically satisfy the required setpoint.This command signal (Vcom) is then transferred to a modulator 102 whichis a PWM control circuit (amd can be aprt pof controller 101) thatconverts this signal (0-10V for example) to a pulse train with a dutycycle (α) directly proportional to this signal. This modulated pulsetrain is then used to command on or off the power switches in aninverter (power circuit) 103, which will produce a voltage signal acrossan output stage 104 whose average is proportional to the duty cycle andthe original command signal from controller 101. Feedback is provided bytransducer 105.

An ideal modulator will produce a pulse train with a duty cycle α thatis directly proportional to the command signal (vcom).α=t_on/T=Gpwm*Vcom, where Gpwm is the pwm gain. FIG. 2. shows the plotfor α and vcom for an ideal pulse width modulator. An ideal continuouslinear relationship between the command and the duty cycle helps thecontrol loop of the entire systems to operate properly and remainsstable regardless of the operating point. The slope (Gpwm) of thisrelationship, contributes to the overall gain of the closed loop controlsystem, and must be taken into account to ensure stability of thissystem. Running at a fixed switching frequency (constant period T) themodulator maintains this relationship by reducing varying the on timet_on (pulse width) making it smaller or larger as needed (hence the termPWM).

FIG. 3 shows a pwm control ramp for a typical pwm control. Pwm controlramp, as used herein, refers to values that change with time and arecompared to a V command, and the comparison is used to change states ofthe output. Such a ramp can be implemented using a saw tooth voltageramp: a capacitor charged by a constant current source and discharged bya much larger current.

Inverter based output circuits offer many advantages, but they do havesome drawbacks. One drawback is that pulse width modulators are not, inpractice, ideal. The power circuit typically includes large transistorsthat take time to turn on and then back off again. T_on can thereforepractically only be reduced to a finite minimum time. PWM minimum ontime as used herein refers to the time it takes the switches being pulsewidth modulated to turn on and then off. Other practical circuitelements may also contribute to this minimum on time such as propagationdelay from one circuit element to another, gate drivers dead times, etc.For example, an inverter with a period of T=10 usec and a PWM minimum ontime of 1 usec, the minimum duty cycle is 10%.

A duty cycle of no less than 10% is sufficient for many weldingapplication but in low output welding, such as low end TIG, a duty cycleof 10% does not provide an output low enough to yield a stableconsistent arc.

U.S. Pat. No. 6,661,679 shows a PWM controller having an adaptiveoff-time modulation. The Miller® Dynasty® 210 and Miller® Maxstar®attempt to address the minimum duty cycle of inverters by adjusting thepulse frequency. Since t_on cannot be reduced below the PWM minimum ontime, T was increased to allow for smaller α. This is referred to asfrequency reduction. This was an improvement over the prior art becauseit allowed for operation at low output.

FIG. 4 shows the prior art implementation of frequency reduction usedfor low output in the Miller® Dynasty®. The period is extended byreducing the discharge current from its normal level in proportion tohow much Vcom is below Vcommand minimum. Vcommand minimum is the commandsignal that provides a pwm on time equal to the PWM minimum on time.This effectively extends the time it takes to reset the ramp down toVmin and therefore stretches the period T. In this schemei_dis*Idis+Kd*Adjusted Vcom, where Adjusted Vcom<0 by definition and Kdis a constant chosen to set the amplitude of the frequency reduction.Adjusted Vcom=Vcom−Vcommand minimum.

One problem with this method for stretching the period is the resultingrelationship between the duty cycle and the command signal becomesnon-linear. FIG. 5 is a graph of a pwm transfer function—Vcom and theduty cycle α for both an ideal PWM and the prior art frequency adjustedPWM. Pwm transfer function, as used herein refers to the duty cyclesprovided for command signals (voltage, current, digital value inside amicroprocessor, etc) over a range of command signals. Not only is theprior art pwm transfer function non linear below the PWM minimum on time(corresponding to Vcom=2 on the graph), there is a discontinuity in theslope of this relationship, which sets the gain of this stage in thesystem, and the slope changes a great deal as the duty cycle is reduced.Because the gain of the PWM stage using prior art frequency reduction isnonlinear, a can oscillate between 2% to 10%—the portion of the curvewhere the gain is the highest. This oscillation can be present in thearc, both visually and audibly.

When maintaining an arc at very low amperage the amount of powertransferred is very low, requiring a low duty cycle. Additionally thearc characteristic at low amperage <10 A tend to be unstable, requiringa properly tuned closed loop control system to keep the arc at a properconstant current and stable. Sudden changes in gain (such as in theprior art control scheme) can lead to instability of the system whenoperating at the lower duty cycle. Low amperage operation can either benot very stable or an effort is made to avoid entering frequencyreduction mode altogether at these operating points.

Another prior art method of reducing the frequency at low output poweris to skip pulses. By skipping every other pulse the frequency is cut inhalf, skipping two pulses cuts the frequency to a third, etc. However,this produces a step wise pwm transfer function and is not linear

TIG welding power sources are expected to output and regulate a verywide range of power outputs: for example the output of one unit canoperate from 20 W to 6000 W providing good, stable current regulationover this entire range. Welding systems for other processes also operateat low output (relative to the maximum output), and have a similar needfor stable operation. However, prior art welding type system also oftenhave a control scheme that, as described above, results in instabilityat lower outputs.

Accordingly, a welding type system with PWM control that can morereadily be stable when providing a low output is desired.

SUMMARY OF THE PRESENT INVENTION

According to a first aspect of the disclosure a welding-type systemincludes an input circuit, a power circuit, and a controller. The inputcircuit receives input power and provides intermediate power. The powercircuit has a power control input and at least one switch that respondsto the control input. The power circuit receives the intermediate powerand provides welding type output power. The controller has a set pointinput and a control output. The control output is connected to the powercontrol input. The control circuit also includes a pwm module thatresponds to the user set point input and provides the control output.The pwm module includes a short duty cycle linearizing module.

According to a second aspect of the disclosure a welding-type systemincludes an input circuit, a power circuit and a controller. The inputcircuit receives input power and provides intermediate power. The powercircuit has a power control input and at least one switch that respondsto the control input. The power circuit receives the intermediate powerand provides welding type output power. The controller has a set pointinput and a control output, and the control output is connected to thepower control input. The control circuit includes a pwm module thatresponds to the user set point input and provides the control output.The pwm module includes a short duty cycle charging ramp module.

According to a third aspect of the disclosure a method of providingwelding-type power includes receiving input power, providingintermediate power, converting the intermediate power, providing weldingtype output power, and controlling the converting by pulse widthmodulating the converter. Pulse width modulating includes, for shorterduty cycles, linearizing a pwm transfer function by providing a pwmtransfer function that is closer to linear than the transfer functionprovided absent linearizing.

The pwm module has a pwm transfer function with a first linear gain andthe short duty cycle linearizing module has a short duty cycle pwmtransfer function with a second linear gain, and the second linear gainis not the first linear gain, in one alternative.

The power circuit is includes an inverter circuit in anotheralternative.

The input circuit power circuit includes a preregulator in oneembodiment.

The short duty cycle linearizing module includes a short duty cyclecharging ramp module in various embodiments, and the short duty cyclecharging ramp module can include at least a part of the short duty cyclelinearizing module.

The short duty cycle charging ramp module includes an active thresholdequal to a command minimum on time for the power circuit in anotherembodiment.

The short duty cycle linearizing module provides an adjusted commandsignal and the control output is responsive to the adjusted commandsignal in various embodiments.

Other principal features and advantages of will become apparent to thoseskilled in the art upon review of the following drawings, the detaileddescription and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is block diagram of a prior art welding system;

FIG. 2 is graph of an ideal pwm transfer function;

FIG. 3 is graph of a prior art pwm control ramp;

FIG. 4 is graph of a prior art adjusted pwm control ramp;

FIG. 5 is graph of a prior art and ideal pwm transfer functions;

FIG. 6 is diagram of a circuit that creates a pwm control ramp;

FIG. 7 is graph of a pwm control ramp;

FIG. 8 is graph of a linearized pwm transfer function;

FIG. 9 is graph of a linearized pwm transfer function; and

FIG. 10 is diagram of a welding type system.

Before explaining at least one embodiment in detail it is to beunderstood that the invention is not limited in its application to thedetails of construction and the arrangement of the components set forthin the following description or illustrated in the drawings. Theinvention is capable of other embodiments or of being practiced orcarried out in various ways. Also, it is to be understood that thephraseology and terminology employed herein is for the purpose ofdescription and should not be regarded as limiting. Like referencenumerals are used to indicate like components.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

While the present disclosure will be illustrated with reference toparticular circuitry and controls, it should be understood at the outsetthat the invention can also be implemented with other circuitry andcontrols, and used for other welding type processes. The preferredembodiment is shown in FIG. 10 and implemented with a welding typesystem 1000 that includes an input circuit 1002, a power circuit 1004,and a controller 1006. The input circuit 102, power circuit 104 andcontroller 106 may be in accordance with the prior art, such as thatshown in U.S. Pat. No. 6,987,242 (Geissler), U.S. Pat. No. 6,115,273(Geissler) and Patent Publication 20090230941 (Vogel), except for thefrequency reduction described herein. Input circuit 1002 is preferably apreregulator, such as that shown in U.S. Pat. No. 6,987,242. Powercircuit 1004 is preferably an inverter, such as that shown in FIG. 1 orU.S. Pat. No. 6,987,242. Controller 1006 can be analog, digital, or acombination thereof, and includes the frequency reduction modulesdescribed below.

One embodiment provides for using the system of FIG. 1, with thecontroller and/or modulator modified to include a pwm module thatfunctions as described below.

Generally, the invention provides for controlling a welding type systemat low power such that it operates in a stable manner. This ispreferably accomplished by linearizing the pwm transfer function atshorter duty cycles. Linearizing the pwm transfer function, as usedherein, refers to providing a pwm transfer function that is closer tolinear than the transfer function provided absent the linearizing Pulseskipping does not linearize the pwm transfer as linearizing the pwmtransfer function is used herein. Shorter duty cycle as used hereinrefers to a duty cycle where the on time would be less than the PWMminimum on time, without a frequency reduction.

One embodiment provides for linearizing the pwm transfer function atshorter duty cycles by changing the slope of the charging ramp when thevoltage command is less than Vcommand minimum. Vcommand minimum is thecommand signal that provides a pwm on time equal to the PWM minimum ontime.

The preferred embodiment includes a pwm module that is similar to priorart pwm modules, but with added components and function. Pwm module, asused herein, refers to a module that provides a pwm control ramp.Module, as used herein, refers to software and/or hardware thatcooperates to perform one or more tasks, and can include digitalcommands, control circuitry, power circuitry, networking hardware, etc.A typical pwm module 600 is shown in FIG. 6, but is modified in a newway to reduce the charging current for shorter duty cycles, after theramp exceeds V_(cmd_tmin)—also called Vcommand minimum. Shorter dutycycle as used herein refers to a duty cycle where the on time would beless than the PWM minimum on time, without a frequency reduction. Newcomponents include an op amp 610, a transistor 612, a resistor 614 and adiode 616.

First, the operation at other than shorter duty cycles will bedescribed. In this range the circuit of FIG. 6 functions as a typicalpwm module. A constant current source 601 charges a capacitor 602. Amuch larger current source 603 discharges capacitor 602. Comparators605, 606 and 607 compare the voltage on capacitor 602 to Vmax, Vmin, andVcom (the command voltage or signal). When constant current source 601is charging capacitor 602 and the voltage on capacitor 602 exceeds Vcomthe output is commanded off. When the voltage on capacitor 602 reachesVmax, current source 603 begins to discharge capacitor 602 and thevoltage rapidly decreases. When the voltage on capacitor 602 decreasesto Vmin the output is commanded on, current source 603 is turned off,and the voltage on capacitor 602 rises, until it exceeds Vcom. Then theprocess repeats. Flip flops 608 and 609 change state as the variousvoltage thresholds are crossed.

When operating at low output power the preferred embodiment linearizesthe pwm transfer function. Specifically, at shorter duty cycles—i.e,where the on time would be less than the PWM minimum on time without afrequency reduction. The preferred embodiment provides that the chargecurrent to the capacitor is reduced after the voltage has reachedV_(cmd_tmin) (for shorter duty cycles). This adjusts the pwm controlramp so that the pwm frequency is reduced, and does so in a continuousand largely linear fashion.

The circuit of FIG. 6 includes a short duty cycle linearizing module 611comprised of op amp 610, transistor 612, resistor 614 and diode 616,that cause the charge current to capacitor is 602 to be reduced afterthe voltage has reached V_(cmd_tmin)—also called Vcommand minimum, andits operation and effect will be described below. Vcommand minimum isthe command signal that provides a pwm on time equal to the PWM minimumon time. Short duty cycle linearizing module, as used herein, refers toa module that is operable for at least some shorter duty cycles andprovides a pwm transfer function that is closer to linear than thetransfer function provided absent the short duty cycle linearizingmodule. Also, short duty cycle linearizing module 611 combined withcurrent source 601 are a short duty cycle charging ramp module. Shortduty cycle charging ramp module, as used herein, refers to a module thatis operable for at least some shorter duty cycles and provides a pwmtransfer function that has a pwm charging ramp with a slope that isreduced as the charge current is reduced when the command is below anactive threshold.

The reduction occurs when the duty cycles are shorter, so that the timeon is the minimum on time. By reducing the ramp slope after this time,the off time is increased, and the duty cycle is decreased. FIG. 7 showsadjusted pwm control ramps for this embodiment. After reachingV_(cmd_tmin), the slope of the charging ramp decreases as the chargecurrent is reduced.

Short duty cycle linearizing module 611 and the short duty cyclecharging ramp module operate as follows in the preferred embodiment. Opamp 610, transistor 612, resistor 614 and diode 616 reduce chargingcurrent to capacitor 602 and adjust Vcommand when operating at shorterduty cycles and when the ramp is above Vcommand minimum. The inputs tothe op amp are V_(cmd_tmin) and the adjusted Vcom. Short duty cyclelinearizing module 611 has an active threshold equal to the commandminimum on time for the power circuit, and is set by the input to op amp610. Alternatives use other circuits to implement the slower chargingrate. Another alternative provides that the ramp and/or Vcom and/oradjusted Vcom are implemented with software. FIG. 6 is an ideal versionof a short duty cycle linearizing module and short duty cycle chargingramp module. In practice, additional components may be used inaccordance with common engineering practices to implement a practicalversion of the simple diagram of FIG. 6.

The circuitry will reduce the charge current in a linear fashion asexplained below:Adj. I_chg=I_chg0+Kc*Adj. V_cmd, where Adj V_cmd=v_cmd-V_(cmd_t min)<0,and I_chg0 is the charge at V_(cmd_t min).Thus:Adj i_chg=I_chg0+Kc*Adj. v_cmdAdj i_chg=I_chg0*(1+A*Adj. v_cmd)

A is defined as A=Kc/I_chg0

Then:T=t_min+C*(V_max-V_(cmd_t min))/(Adj. i_chg)+t_dischT=t_min+C*(V max-V_(cmd_t min))/(I_chg*(1+A*Adj. v_cmd))+t_discht_max is defined as t_max=C(V max−V_(cmd_t min))/I_chg0,then t_max=t_charge0−t_minand T0=t_charge0+t_disch

This gives a period T of:T=t_min+t_max/((1+A*Adj. v_cmd))+t_disch

From this the duty cycle in frequency reduction mode can be calculated:α(Adj. v_cmd)=t_min/(t_min+t_max/((1+A*Adj. v_cmd))+t_disch)α(Adj. v_cmd)=(t_min(1+A*Adj. v_cmd))/((t_min+t_disch)(1+A*Adj.v_cmd)+t_charge0−t_min)α(Adj. v_cmd)=(t_min(1+A*Adj. v_cmd))/((t_min+t_disch)(A*Adj.v_cmd)+(t_charge0+t_disch))α(Adj. v_cmd)=(t_min(1+A*Aadj. v_cmd))/((t_min+t_disch)(A*Adj.v_cmd)+T_0)And, (A*Adj. v_cmd)ε[−1,0], and if both t_min and t_disch<<T_0

Then the relationship between duty cycle and command voltage isapproximated to: α(Adj. v_cmd)=(t_min/T_0)*(1+A*Adj. v_cmd)

The pwm transfer function for this embodiment (the relationship betweenα and Adj. v_cmd) is plotted in FIG. 8, along with the ideal pwmtransfer function, and as can be seen the pwm transfer function for thisembodiment is linearalized.

The slope of the relationship (gain of the system) is almost constantover the entire range. With the same simplifying assumptions as above,dα/dAdj. v_cmd=(A*t_min*T_0)/(T_0)² =A*t_min/T_0This gain is constant and by selection of the parameter A the slope thefrequency reduction can be made to match that of the modulator in thenormal mode, therefore offering a good transition between normaloperation and frequency reduction modes (i.e, above and below Vcommandminimum. This difference between the ideal transfer function and onedescribed herein is 0 at V_(cmd_tmin) and 0V. The maximum differenceoccurs at a command voltage of (Adj. v_com) diffmax=(−T_0+sqrt(T_0*(T_0−t_min−t_disch)))/(t_min+t_disch)*A

Circuit parameters that the inventor has found work well and were usedfor the graph of FIG. 8 include capacitor 601=1 nF, Vmax=10V, Vmin=0V,Vcmd_min (Vcommand minimum)=2V, Icharge=1 mA, B=30 (Discharge to chargeratio), Kd=15 mA/V (Discharge reduction rate), and Kc=0.5 mA/V (Chargereduction rate set by resistor 614), with A=0.5 l/V.

Other parameters can be chosen, to maintain a linear relationship suchas that shown in FIG. 8. Choosing the parameter A=K c/I_chg0 so thatA*V_(cmd_tmin)=1 gives a largely linear relationship. The duty cyclewill then decrease down to 0% at 0V of Vcmd. Alternatively, the shortduty cycle linearizing module could be implemented to have the gainchange slightly at light load. This could be used to adapt to theoverall gain of the system which can change with different arcconditions. A different value of the A parameter can accomplish this.Choosing A lower than ideal will reduce the gain, but the duty cyclewill not reach 0 at 0V command. This is illustrated in FIG. 9 withA*V_(cmd_tmin)=0.7. Other alternatives provide for other pwm transferfunctions

Numerous modifications may be made to the present disclosure which stillfall within the intended scope hereof. Thus, it should be apparent thatthere has been provided a method and apparatus for a welding type systemwith frequency reduction and linearized pwm transfer function that fullysatisfies the objectives and advantages set forth above. Although thedisclosure has been described specific embodiments thereof, it isevident that many alternatives, modifications and variations will beapparent to those skilled in the art. Accordingly, the invention isintended to embrace all such alternatives, modifications and variationsthat fall within the spirit and broad scope of the appended claims.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined as follows:
 1. A welding-type systemcomprising: an input circuit disposed to receive input power and toprovide intermediate power; a power circuit, having a power controlinput and at least one switch responsive to the power control input, andwherein the power circuit is disposed to receive intermediate power andprovide welding type output power; a controller, having a set pointinput and a control output, wherein the control output is connected tothe power control input, and wherein the control circuit includes a pwmnodule responsive to the set point input and providing the controloutput, wherein the pwm module includes a short duty cycle linearizingmodule.
 2. The welding-type system of claim 1, wherein the pwm modulehas a pwm transfer function with a first linear gain and the short dutycycle linearizing module has a short duty cycle pwm transfer functionwith a second linear gain, wherein the second linear gain is not thefirst linear gain.
 3. The welding-type system of claim 2, wherein thepower circuit is includes an inverter circuit.
 4. The welding-typesystem of claim 3, wherein the input circuit power circuit includes apreregulator.
 5. The welding-type system of claim 1, wherein the shortduty cycle linearizing module includes a short duty cycle charging rampmodule.
 6. The welding-type system of claim 5, wherein the short dutycycle charging ramp module includes an active threshold equal to acommand minimum on time for the power circuit.
 7. The welding-typesystem of china 1, wherein the short duty cycle linearizing moduleprovides an adjusted command signal and the control output is responsiveto the adjusted command signal.
 8. A welding-type system comprising: aninput circuit disposed to receive input power and to provideintermediate power; a power circuit, having a power control input and atleast one switch responsive to the power control input, and wherein thepower circuit is disposed to receive intermediate power and providewelding type output power; a controller, having a set point input and acontrol output, wherein the control output is connected to the powercontrol input, and wherein the control circuit includes a pwm moduleresponsive to the set point input and providing the control output,wherein the pwm module includes a short duty cycle linearizing moduleand a short duty cycle charging ramp module.
 9. The welding-type systemof claim 8, wherein the short duty cycle charging ramp module includesan active threshold equal to a command minimum on time for the powercircuit.
 10. The welding-type system of claim 9, wherein the powercircuit is includes an inverter circuit.
 11. The welding-type system ofclaim 10, wherein the input circuit power circuit includes apreregulator.
 12. The welding-type system of claim 11, wherein the pwmmodule includes a short duty cycle linearizing module, and the shortduty cycle charging ramp module is at least a portion of the short dutycycle linearizing module.
 13. The welding-type system of claim 12,wherein the pwm module has a pwm transfer function with a first lineargain and the short duty cycle linearizing module has a short duty cyclepwm transfer function with a second linear gain, wherein the secondlinear gain is not the first linear gain.